Length units

🏆Practice length units

Units of length allow us to quantify length, height and distance.

Units of length to know.

A centimeter is equivalent to 10 10 millimeters.

A meter is equivalent to 100 100 centimeters.

One kilometer is equal to 1000 1000 meters.

A1 - Length units

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Test yourself on length units!

Convert to meters:
\( 40 \) cm

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Example of an exercise with units of length

How many centimeters are there in 1.56 meters?

Here the calculation is quite simple.
If one meter is equivalent to 100 100 centimeters we should multiply it by 100 100 to get the number of centimeters.
1.56100=156 1.56\cdot100=156

That is, 1.56 1.56 meters equals 156 156 centimeters.


Another exercise with units of length

Sometimes we will have to solve exercises in which we will have to convert a unit to a much smaller one. In this case we will make an intermediate calculation and go through a unit that is "in the middle".

For example, how many centimeters are there in 2 kilometers?

We know that one kilometer is equivalent to 1000 1000 meters.

Therefore, we will first convert kilometers to meters and then meters to centimeters.

1km=1000 1 km = 1000 meters

2km= 2 km = meters?

We will multiply the 2 2 km by 1000 1000 :

21000=2000 2\cdot1000=2000

Therefore, 2 2 km equals 2000 2000 meters.

Now we will make the conversion to centimeters.

1metro=100cm 1 metro = 100 cm .

2000metros= 2000 metros = centimeters?

We will multiply the 2000 2000 m by 100 100 and we get:

2000100=200,000 2000\cdot100=200,000

Therefore, 2 2 km equals 200,000 200,000 cm.

Another way is to multiply directly: knowing that to convert kilometers to meters you multiply by 1000 1000 and to convert meters to centimeters you multiply by 100 100 , we can multiply 1000×100 1000\times100 , that is, multiply directly by 100,000 100,000 .

We recommend doing it step by step to avoid confusion :)


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Review questions

What is the concept of length?

Length can be defined as the part that measures an object from one side to another, that is, the distance between one point to another, the unit in the International System (SI) is meters, that is, we can measure the length of an object usually in meters, but there are also units of equivalence to this unit, such as centimeters, millimeters, hectometers, decameters and kilometers.


What are the instruments for measuring length?

There are different instruments to measure the length of an object or in other words the dimension or distance from one point to another, some of the most common instruments are the following:

  • Ruler
  • Measuring tape
  • Tape measure
  • Square
  • Caliper

What is a unit of length?

A unit of measure will be the one that we will use as a reference to measure and quantify an object, in the case of the unit of length is the meter by the International System of Units. The meter is the unit of reference most frequently used to measure the length of an object.


How many centimeters are 27.5 27.5 meters?

For this exercise we must know that centimeters and meters are units of measurement that are multiples, i.e. in this case 1m=100cm 1m=100\operatorname{cm}

So if a meter has 100 100 centimeters, then let's make a multiplication

27.5×100cm=2750cm 27.5\times100\operatorname{cm}=2750\operatorname{cm}

Then 27.5m 27.5m equals 2750cm 2750\operatorname{cm}


How many centimeters are equal to 36.8 36.8 inches?

In this case we must keep in mind that 1pulgada=2.52cm 1\text{pulgada}=2.52\operatorname{cm} , so for this exercise let's do a multiplication

36.8×2.52cm=92.736cm 36.8\times2.52\operatorname{cm}=92.736\operatorname{cm}

Therefore 36.8 36.8 inches equals 92.736 92.736 centimeters.

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Ejemplos y ejercicios con soluciones de וnidades de longitud

Exercise #1

Convert to meters:
40 40 cm

Step-by-Step Solution

To solve this problem, let's convert the measurement from centimeters to meters by following these steps:

  • Identify the given measurement: 40 40 cm.
  • Recall the conversion factor: 1 1 meter = 100 100 centimeters.
  • Apply the conversion factor to convert 40 40 cm into meters by dividing by 100 100 :
    40100=0.4\frac{40}{100} = 0.4 meters.

This calculation shows that 40 40 cm is equivalent to 0.4 0.4 meters.

Therefore, the solution to the problem is 0.4 0.4 .

Answer

0.4 0.4

Exercise #2

Which of the following values equals:
5000 5000 cm

Step-by-Step Solution

To solve the problem, let's follow these steps:

  • Step 1: Convert centimeters to meters.
  • Step 2: Identify the correct answer from the given choices.

Now, let's work through each step:

Step 1: We know that 1 meter=100 cm1 \text{ meter} = 100 \text{ cm}. Therefore, to convert 50005000 cm to meters, we divide 50005000 by 100100:

5000100=50 \frac{5000}{100} = 50 meters.

Step 2: Among the given choices, we are looking for 5050 meters, which matches Choice 4\text{Choice 4}.

Therefore, the solution to the problem is 50 50 m.

Answer

50 50 m

Exercise #3

Convert to cm:
0.6 0.6 meters

Step-by-Step Solution

To solve the problem of converting meters to centimeters, we apply the following steps:

  • Step 1: Identify the given value, which is 0.6 meters.
  • Step 2: Use the conversion factor between meters and centimeters. There are 100 centimeters in one meter, so the formula is centimeters=meters×100 \text{centimeters} = \text{meters} \times 100 .
  • Step 3: Multiply 0.6 meters by 100 to convert it to centimeters.

Let's carry out the calculation:
0.6 meters ×\times 100 = 60 centimeters.

Therefore, the conversion of 0.6 meters to centimeters is 60 60 centimeters.

Answer

60 60

Exercise #4

Calculate the surface area of the box shown in the diagram.

Pay attention to the units of measure!

5 dm5 dm5 dm4 cm4 cm4 cm0.3 dm0.3 dm0.3 dm

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert all dimensions to the same unit.

  • Step 2: Apply the surface area formula for a cuboid.

  • Step 3: Calculate the total surface area.

Now, let's work through each step:

Step 1: Convert all dimensions to the same unit. For consistency, we will convert everything to decimeters (dm):

  • Width = 5 dm (already in dm)

  • Height = 4 cm. To convert cm to dm, divide by 10: 4cm=0.4dm 4 \, \text{cm} = 0.4 \, \text{dm} .

  • Depth = 0.3 dm (already in dm)

Step 2: Apply the surface area formula for a cuboid:

The surface area A A is given by:

A=2lw+2lh+2wh A = 2lw + 2lh + 2wh

Where:

  • l=0.3dm l = 0.3 \, \text{dm} (depth)

  • w=5dm w = 5 \, \text{dm} (width)

  • h=0.4dm h = 0.4 \, \text{dm} (height converted to dm)

Substitute these values into the formula:

A=2(0.3)(5)+2(0.3)(0.4)+2(5)(0.4) A = 2(0.3)(5) + 2(0.3)(0.4) + 2(5)(0.4)

Step 3: Calculate the surface area:

A=2(1.5)+2(0.12)+2(2) A = 2(1.5) + 2(0.12) + 2(2)

A=3+0.24+4 A = 3 + 0.24 + 4

A=7.24dm2 A = 7.24 \, \text{dm}^2

Note that the question requires the surface area in different units.

Thus, 7.24 dm² is 72.4 cm²

Therefore, the solution to the problem is 72.4 cm².

Answer

72.4 cm²

Exercise #5

Order from smallest to largest:

0.03 0.03 m, 5 5 cm, 25 25 mm, 0.001 0.001 dm

Step-by-Step Solution

To solve this problem, we need to convert all the given lengths to a common unit of measurement, here we'll use meters.

First, let's convert each measurement to meters:

  • 0.030.03 m is already in meters.
  • 55 cm: Since 1 cm=0.01 m1 \text{ cm} = 0.01 \text{ m}, then 5 cm=5×0.01 m=0.05 m5 \text{ cm} = 5 \times 0.01 \text{ m} = 0.05 \text{ m}.
  • 2525 mm: Since 1 mm=0.001 m1 \text{ mm} = 0.001 \text{ m}, then 25 mm=25×0.001 m=0.025 m25 \text{ mm} = 25 \times 0.001 \text{ m} = 0.025 \text{ m}.
  • 0.0010.001 dm: Since 1 dm=0.1 m1 \text{ dm} = 0.1 \text{ m}, then 0.001 dm=0.001×0.1 m=0.0001 m0.001 \text{ dm} = 0.001 \times 0.1 \text{ m} = 0.0001 \text{ m}.

Next, we compare the values we have in meters:

  • 0.00010.0001 m (from 0.0010.001 dm)
  • 0.0250.025 m (from 2525 mm)
  • 0.030.03 m
  • 0.050.05 m (from 55 cm)

Thus, ordering from smallest to largest is: 0.0010.001 dm, 2525 mm, 0.030.03 m, 55 cm.

Therefore, the correct order from smallest to largest is:

0.001 0.001 dm
25 25 mm
0.03 0.03 m
5 5 cm

Answer

0.001 0.001 dm
25 25 mm
0.03 0.03 m
5 5 cm

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